Six bells commerce tolling together and they toll at intervals of 2, 4, 6, 8,…
2025
Six bells commerce tolling together and they toll at intervals of 2, 4, 6, 8, 10 & 12 sec respectively. In 30 minutes, how many times do they toll together ?
- A.
4
- B.
10
- C.
15
- D.
16
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Step-by-Step Calculation
1. Find the LCM of the intervals:
The intervals are 2, 4, 6, 8, 10, and 12 seconds.
Prime factorization:
2 = 2
4 = 2^2
6 = 2 * 3
8 = 2^3
10 = 2 * 5
12 = 2^2 * 3
Taking the highest power of each prime factor present (2^3, 3^1, 5^1):
LCM = 8 * 3 * 5 = 120 seconds.
This means the bells toll together every 120 seconds, or every 2 minutes.
2. Calculate the number of intervals in the total duration:
Total time = 30 minutes.
Number of intervals = Total time / Interval time = 30 / 2 = 15 intervals.
3. Account for the initial toll:
Since the bells start by tolling together at time zero, we must add that initial event to the 15 intervals that occur during the 30-minute duration.
Total tolls = 15 + 1 = 16 times.